The National Bank of Tuvalu is the country's only bank, the only place to change foreign currency, and one of two ATMs in the country. It is housed in a low concrete building in Vaiaku and keeps short, irregular hours. Bring cash — Australian dollars are the currency, US dollars are sometimes accepted at the bank, and card facilities barely exist outside this building.
You will probably need to visit at some point if you are staying more than a few days. Treat it as an outing: the queue is part of village life, you will meet half the people you have already met that week, and the visit will take longer than it strictly needs to. That is how things work here.